Fresh speculation about Scott Brown‘s possible hopes to return to the Senate from his new base in New Hampshire swirled Wednesday, as a poll showed that he remains within striking distance of the incumbent, Democratic Sen. Jeanne Shaheen, should he run.

The new Public Policy Polling survey shows Ms. Shaheen would hold a narrow lead of three percentage points over Mr. Brown if the onetime senator from Massachusetts decides to enter the New Hampshire race.

The numbers in the potential race have changed little since PPP last conducted a poll in September. Ms. Shaheen leads other Republican candidates by much wider margins. She has a 14-point lead over former New Hampshire Sen. Bob Smith, a 16-point lead over former state Sen. Jim Rubens, and a 17-point lead over former gubernatorial candidate Karen Testerman.

New Hampshire Republicans overwhelmingly preferred Mr. Brown as their candidate than the other contenders, with 42% saying he would be their choice, compared to 11% for Mr. Smith, 8% for Mr. Rubens, and 7% for Ms. Testerman.

The poll, which surveyed 1,354 New Hampshire voters—including 528 Republican primary voters—from Jan. 9-12, has a margin of error of plus or minus 2.7 percentage points. The margin of error for the Republican primary part is plus or minus 4.3 percentage points.

Though Mr. Brown has not formally entered the race, he is widely believed to be considering a bid. Further fueling those rumors is a new website in his name featuring his photo with the slogan “giving power back to the people.” The site includes a link to email the former senator and says a full website will be coming soon. It wasn’t clear when the new placeholder site went up; it was mentioned on Twitter last week but first gained wider attention on Wednesday.

Mr. Brown didn’t respond to a request for comment.

Mr. Brown made waves in the Twittersphere in November for dropping “MA” from his Twitter handle, which is now @SenScottBrown.

In December, Mr. Brown found a buyer for his home in Wrentham, Mass., and said he planned to move his primary residence to his home in New Hampshire.

About Washington Wire

Washington Wire is one of the oldest standing features in American journalism. Since the Wire launched on Sept. 20, 1940, the Journal has offered readers an informal look at the capital. Now online, the Wire provides a succession of glimpses at what’s happening behind hot stories and warnings of what to watch for in the days ahead. The Wire is led by Reid J. Epstein, with contributions from the rest of the bureau. Washington Wire now also includes Think Tank, our home for outside analysis from policy and political thinkers.